Answer
(a) $905~ft^2$
(b) $407.25
(c) 152 flowers are needed.
Work Step by Step
(a) We can find the area of a semicircle with a radius of $30~ft$:
$A_2 = \frac{1}{2}\pi~r^2$
$A_2 = \frac{1}{2}\pi~(30~ft)^2$
$A_2 = 1413.7~ft^2$
We can find the area of a semicircle with a radius of $18~ft$:
$A_1 = \frac{1}{2}\pi~r^2$
$A_1 = \frac{1}{2}\pi~(18~ft)^2$
$A_1 = 508.9~ft^2$
We can find the area that needs to be resealed:
$A = A_2-A_1 = (1413.7~ft^2)-(508.9~ft^2) = 905~ft^2$
(b) We can find the cost of resealing the driveway:
$cost = (\$0.45/ft^2)(905~ft^2) = \$407.25$
(c) We can find the length of a semicircle with a radius of $31~ft$:
$L_2 = \pi~r = \pi~(31~ft) = 97.4~ft$
We would plant one flower at the start and then 97 more flowers around the outside edge of the driveway. We could plant 98 flowers around the outside.
We can find the length of a semicircle with a radius of $17~ft$:
$L_1 = \pi~r = \pi~(17~ft) = 53.4~ft$
We would plant one flower at the start and then 53 more flowers along the inside edge of the driveway. We could plant 54 flowers along the inside.
The total number of flowers is $98+54$ which is $152$ flowers.
